完全正则狭义拟仿紧空间的逆极限及Tychonoff乘积定理

Inverse limits and Theorems of Tychonoff Products of Completely Regular Strict Quasi-Paracompactness Spaces

狭义拟仿紧空间是广义仿紧空间类的重要空间,文章在附加完全正则的条件下讨论了狭义拟仿紧空间的逆极限定理和Tychonoff乘积定理,得到以下主要结论:(1)设X=←lim{xσ,πσρ,Σ},并且每一个投射πσ:Χ→Xσ是开满射,设X是Σ-仿紧空间,其中Σ>2,若每一个Χσ是完全正则狭义拟仿紧空间,则Χ也是完全正则狭义拟仿紧空间;(2)记X=∏α∈ΛXα是Λ-仿紧空间,则Χ是完全正则狭义拟仿紧空间当且仅当σ∈Σ,Χ=∏α∈σΧα是完全正则狭义拟仿紧空间,其中:Σ=Λ。文章的证明方法以及得出的结论使狭义拟仿紧空间的逆极限的保持性及其乘积性更加清楚,同时所讨论的内容也使得狭义拟仿紧空间类的一些性质在应用时更加方便。

The Strict Quasi-Paracompaetness space is an important space of generalized paracompact spaces. Based on the additional condition that the Strict Quasi-Paracompactness space is completely regular space, the inverse limit and Yychonoff product theorem are discussed, the main conclusions are the following： （1）let X=lim{xσ,πρσ,∑} and let every projection tribe open and onto mapping, if X is ｜∑｜ -paracompact space and every xσ is Completely regular Strict Quasi-Para- compactness space,｜∑｜〉2, then X is Completely regular Strict Quasi-Paracompactness space. （2）let X=∏a∈∧Xα be ｜∧｜ -paracompact space, only if A↓Vσ∈∑,X=∏a∈σ is Completely regular Strict Quasi-Paracompactness space, ∑=｜∧｜, then X is Completely regular Strict Quasi-Paracompactness space. From the proof method and conclusions, the retentivity of inverse limit and products of Strict Quasi-Paracompactness spaces are more clearly, also the content discussed makes some properties of Strict Quasi-Paracompactness spaces more convenient in application.